Sensorless control method for motor and system using the same

ABSTRACT

A sensorless control method for a motor performed by a sensorless controller including a back electromotive force (EMF) observer and a phase locked loop (PLL) controller, includes: estimating a back EMF of the motor using the back EMF observer; calculating an electrical angle error in accordance with iron loss of the motor based on the estimated back EMF; and compensating for the calculated electrical angle error, inputting the compensated electrical angle error into the PLL controller to estimate an actual angle, and controlling the motor based on the estimated actual angle.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2014-0073080 filed in the Korean IntellectualProperty Office on Jun. 16, 2014, the entire contents of which areincorporated herein by reference.

BACKGROUND

(a) Technical Field

The present disclosure relates to a sensorless control method for amotor and a system using the same, and more particularly, to asensorless control method for a motor and a system using the same thatmay stably perform sensorless control in an ultra-high-speed drivingregion of a motor by adding a control model based on iron loss of themotor to a back electromotive force (back EMF) observer, and byobtaining an accurate electrical angle error based on the iron lossthrough the control model.

(b) Description of the Related Art

As is known in the art, a motor applied to an electrical turbocharger istypically very small and thus may be greatly influenced bycharacteristic loss thereof. Accordingly, while the motor is driven by aconventional sensorless control method, an electrical angle errorthereof increases in an ultra-high-speed driving region, and thus, themotor is not able to be controlled according to an accurate angle,thereby resulting in an uncontrolled situation.

Referring to FIG. 1, which illustrates a controller for a typicalpermanent magnet electric motor, a sensorless control method observesthe back EMF using a measured phase current, d-axis, q-axis voltage, andcurrent commands estimated from the measured phase current to obtain anelectrical angle error (Δθ). A phase-locked loop (PLL) controller isused to change the obtained electrical angle error to zero. Estimatedangular velocity information may be obtained from output of thephase-locked loop controller in which the obtained electrical angleerror is eliminated, and it may be used in a vector control of themotor.

To obtain an accurate electrical angle error, it is necessary todetermine the back EMF, and the determination of the back EMF may beobtained from the motor model. Generally, a motor model which does notconsider iron loss is used, which is not suitable for controlling anultra-high-speed motor, at which significantly iron loss occurs. Thus, alarge electrical angle error is caused when controlling theultra-high-speed motor, making the conventional sensorless controlmethod unstable because of the large electrical angle error thatresults. Therefore, it is difficult to perform the sensorless control inan ultra-high-speed driving region of about 50,000 rpm or more.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the disclosure, andtherefore, it may contain information that does not form theconventional art that is already known in this country to a person ofordinary skill in the art.

RELATED ART DOCUMENT Patent Document

(Patent Document 1) Japanese Laid-Open Patent Publication No.P2012-166776 (Sep. 6, 2012)

SUMMARY

Accordingly, the present disclosure has been made in an effort toprovide a sensorless control method for a motor and a system using thesame that may stably perform sensorless control in a ultra-high-speeddriving region of a motor by adding a control model based on iron lossof the motor to a back electromotive force (back EMF) observer and byobtaining an accurate electrical angle error based on the iron loss.Further, the present disclosure has been made in an effort to provide asensorless control method for a motor and a system using the same inwhich iron loss of a motor may be determined by a back EMF observer andmay compensate an EMF of the motor based on the determined iron loss,calculate an accurate electrical angle error using the compensated EMF,and then use the accurate electrical angle error in control of themotor.

Emdbodiments of the present disclosure provide a sensorless controlmethod for a motor performed by a sensorless controller which includes aback electromotive force (EMF) observer and a phase locked loop (PLL)controller, including: estimating a back EMF of the motor using the backEMF observer; calculating an electrical angle error in accordance withiron loss of the motor based on the estimated back EMF; compensating forthe calculated electrical angle error; inputting the compensatedelectrical angle error into the PLL controller to estimate an actualangle; and controlling the motor based on the estimated actual angle.

The voltages (v_(γ), v_(δ)) of the motor based on the iron loss may becalculated using the equation below.

$\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + {\quad{\begin{bmatrix}{{\frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} \\{{\frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}}\end{bmatrix} = \mspace{11mu}{{e_{\gamma\delta}^{\prime}\mspace{20mu} E_{ex}} = {{\omega_{e}\left\lbrack {{\left( {L_{d} - L_{q}} \right)i_{d}} + \psi_{m}} \right\rbrack} - {\left( {L_{d} - L_{q}} \right)\left( {pi}_{q} \right)}}}}}}}}$

d, q: accurate d, q-axis

ω_(e): electric angular velocity of motor

i_(d): d-axis current

i_(q): q-axis current

i_(di): d-axis iron loss current

i_(qi): q-axis iron loss current

i_(dm): d-axis magnetizing current

i_(qm): q-axis magnetizing current

v_(d): d-axis voltage

v_(q): q-axis voltage

R_(s): stator phase resistance

R_(i): Iron loss equivalent resistance

L_(d): d-axis inductance

L_(q): q-axis inductance

ψ_(m): permanent magnet flux constant

P_(iron): Iron loss

P_(h): hysteresis loss

P_(ed): eddy-current loss

e_(γ): estimated d-axis extended EMF

e_(δ): estimated q-axis extended EMF

e′_(γ): estimated d-axis extended EMF considering iron loss

e′_(δ): estimated q-axis extended EMF considering iron loss

The back EMF observer may estimate the voltages (v_(γ), v_(δ)) using theequation below.

$\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}^{\prime}\end{bmatrix}}}}$

The electrical angle error (Δθ+α) may be calculated using the equationbelow.

$e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}$$e_{\delta}^{\prime} = {{{\frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}$$\mspace{79mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{14mu}\alpha} = {\tan^{- 1}\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}}}$

The inputting of the compensated electrical angle error into the PLLcontroller to estimate the actual angle may include reducing theelectrical angle error based on the iron loss.

Further, embodiments of the present disclosure provides a sensorlesscontrol system controlling a motor which includes a permanent magnetmotor, including: a back EMF observer configured to estimate a back EMFof the motor; an angle error calculator configured to calculate anelectrical angle error in accordance with iron loss of the motor basedon the estimated back EMF; an angle error compensator configured tocompensate for the calculated electrical angle error; and a PLLcontroller configured to: i) receive the compensated electrical angleerror, ii) estimate an actual angle, and iii) control the motor based onthe estimated actual angle.

The back EMF observer may be further configured to estimate voltages(v_(γ), v_(δ)) using the equation below.

$\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {{\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix}} + \begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}\end{bmatrix}}$

The angle error calculator may be further configured to calculate theelectrical angle error (Δθ+α) using the equation below.

$e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}$$e_{\delta}^{\prime} = {{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}$$\mspace{20mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{34mu}\alpha} = {\tan^{- 1}\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}}}$

The PLL controller may be further configured to estimate the actualangle by reducing the electrical angle error based on the iron loss.

As described above, according to embodiments of the present disclosure,it is possible to stably perform sensorless control in anultra-high-speed driving region of a motor by adding a control modelbased on iron loss of the motor to a back electromotive force (back EMF)observer and by obtaining an accurate electrical angle error inaccordance with the iron loss using the control model. According toembodiments of the present disclosure, it is possible to determine theiron loss of a motor by a back EMF observer, to compensate for an EMF ofthe motor based on the determined iron loss, to calculate an accurateelectrical angle error using the compensated EMF, and to use theaccurate electrical angle error in order to control the motor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a controller for controllinga typical permanent magnet motor.

FIG. 2 is a diagram illustrating a sensorless control system forcontrolling a permanent magnet motor according to embodiments of thepresent disclosure.

FIG. 3 is a flowchart showing a sensorless control method forcontrolling a permanent magnet motor according to embodiments of thepresent disclosure.

FIG. 4 is a table drawing for comparing a control model for a permanentmagnet motor based on iron loss with a control model therefor not basedon iron loss.

FIG. 5 is a graph illustrating a voltage equation for a motor accordingto embodiments of the present disclosure.

FIG. 6 is a schematic drawing for comparing an internal logic of a backEMF observer according to embodiments of the present disclosure with aconventional internal logic thereof.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure will be described more fully hereinafter withreference to the accompanying drawings, in which embodiments of thedisclosure are shown. As those skilled in the art would realize, thedescribed embodiments may be modified in various different ways, allwithout departing from the spirit or scope of the present disclosure.

In addition, in the specification, unless explicitly described to thecontrary, the word “comprise” and variations such as “comprises” or“comprising” will be understood to imply the inclusion of statedelements but not the exclusion of any other elements.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the disclosure.As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items.

It is understood that the term “vehicle” or “vehicular” or other similarterm as used herein is inclusive of motor vehicles in general such aspassenger automobiles including sports utility vehicles (SUV), buses,trucks, various commercial vehicles, watercraft including a variety ofboats and ships, aircraft, and the like, and includes hybrid vehicles,electric vehicles, plug-in hybrid electric vehicles, hydrogen-poweredvehicles and other alternative fuel vehicles (e.g. fuels derived fromresources other than petroleum). As referred to herein, a hybrid vehicleis a vehicle that has two or more sources of power, for example bothgasoline-powered and electric-powered vehicles.

Additionally, it is understood that one or more of the below methods, oraspects thereof, may be executed by at least one controller. The term“controller” may refer to a hardware device that includes a memory and aprocessor. The memory is configured to store program instructions, andthe processor is configured to execute the program instructions toperform one or more processes which are described further below.Moreover, it is understood that the below methods may be executed by anapparatus comprising the controller, whereby the apparatus is known inthe art to be suitable for performing a sensorless control method for amotor, as described herein.

FIG. 2 is a diagram illustrating a sensorless control system forcontrolling a permanent magnet motor according to embodiments of thepresent disclosure.

Referring to FIG. 2, a sensorless control system for controlling a motor(e.g., a permanent magnet motor) according to embodiments of the presentdisclosure includes: a back EMF observer 110 configured to estimate aback EMF of a motor 10; an angle error calculator 120 configured tocalculate an electrical angle error in accordance with iron loss of themotor 10 based on the back EMF estimated by the back EMF observer 110;an angle error compensator 130 configured to compensate the electricalangle error calculated by the angle error calculator 120; and a PLLcontroller 150 configured to receive the compensated electrical angleerror, to estimate an actual angle by reducing the electrical angleerror due to the iron loss in the PLL controller 150, and to control themotor 10 based on the estimated actual angle.

Symbols denoted in FIG. 2 are referred to as definition as follows:

γ, δ: estimated d-axis, q-axis

ω_(m)*: mechanical angular velocity command value of motor

ω_(m): estimated mechanical angular velocity of motor (sensorlesscontrol result value thereof)

θ: estimated electrical angular velocity (sensorless control resultvalue thereof)

Δθ: electrical angular velocity error

i_(γ)*: estimated d-axis current command value

i_(δ)*: estimated q-axis current command value

i_(γ): estimated measured d-axis current (current measured by3-phase/2-phase converter after current sensor)

i_(δ): estimated measured d-axis current (current measured by3-phase/2-phase converter after current sensor)

v_(γ)*: estimated d-axis voltage command value

v_(δ)*: estimated q-axis voltage command value

t_(a)t_(b)t_(c): PWM ON times for a, b, c phases

i_(b), i_(c): currents for b, c phases (or, it is allowable to measureany 2-phase currents among the 3-phase currents.)

ê_(γ): extended estimated d-axis EMF value (result of observer)

ê_(δ): extended estimated q-axis EMF value (result of observer)

In embodiments of the present disclosure, the motor 10 may be apermanent magnet electric motor such as a motor applied to an electricalturbocharger system, but it should be understood that the scope of thepresent disclosure is not limited thereto.

The sensorless control system according to embodiments of the presentdisclosure may include the back EMF observer 110, the angle errorcalculator 120, the angle error compensator 130, and the PLL controller150, as well as a weak magnetic flux controller 11, a d-axis currentcontroller 13, a vector controller 15, an inverter 17, a velocitycontroller 23, a q-axis current controller 25, and a 3-phase/2-phaseconverter 21 as shown in FIG. 1 illustrating the controller forcontrolling the typical permanent magnet motor.

In embodiments of the present disclosure, the weak magnetic fluxcontroller 11, the d-axis current controller 13, the vector controller15, the inverter 17, the velocity controller 23, the q-axis currentcontroller 25, and/or the 3-phase/2-phase converter 21 may be the sameas or similar to those used in the related art, and thus a detaileddescription thereof will be omitted.

Meanwhile, voltages (v_(γ), v_(δ)) of the motor 10 may be calculated bythe following equations.

$\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{w_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \mspace{371mu}\left\lbrack \begin{matrix}{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} \\{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}}\end{matrix} \right\rbrack} = {{e_{\gamma\delta}^{\prime}\mspace{79mu} E_{ex}} = {{\omega_{e}\left\{ {{\left( {L_{d} - L_{q}} \right)i_{d}} + \psi_{m}} \right\}} - {\left( {L_{d} - L_{q}} \right)\left( {pi}_{q} \right)}}}}}}$

d, q: accurate d, q-axis

ω_(e): electric angular velocity of motor

i_(d): d-axis current

i_(q): q-axis current

i_(di): d-axis iron loss current

i_(qi): q-axis iron loss current

i_(dm): d-axis magnetizing current

i_(qm): q-axis magnetizing current

v_(d): d-axis voltage

v_(q): q-axis voltage

R_(s): stator phase resistance

R_(i): Iron loss equivalent resistance

L_(d): d-axis inductance

L_(q): q-axis inductance

ψ_(m): permanent magnet flux constant

P_(iron): Iron loss

P_(h): hysteresis loss

P_(ed): eddy-current loss

e_(γ): estimated d-axis extended EMF

e_(δ): estimated q-axis extended EMF

e′_(γ): estimated d-axis extended EMF considering iron loss

e′_(δ): estimated q-axis extended EMF considering iron loss

Voltage (v_(γ), v_(δ)) inputted to the back EMF observer 110 maycalculated by the following equation.

$\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {{\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix}} + \begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}\end{bmatrix}}$

In addition, the angle error calculator 120 may calculate an electricalangle error (Δθ+α) using the following equations.

$e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}$$e_{\delta}^{\prime} = {{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}$$\mspace{20mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{34mu}\alpha} = {\tan^{- 1}\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}}}$

A sensorless control method for method for controlling a permanentmagnet motor will now be described in detail with reference to theaccompanying drawings.

FIG. 3 is a flowchart showing a sensorless control method forcontrolling a permanent magnet motor according to embodiments of thepresent disclosure.

As shown in FIG. 3, the back EMF observer 110 estimates a back EMF ofthe motor 10 (S100), and the angle error calculator 120 calculates anelectrical angle error (Δθ+α) due to iron loss of the motor 10 (S200).The electrical angle error (Δθ+α) includes an electrical angle error(Δθ; FIG. 1) according to the related art and an error (α) consideringiron loss of the motor 10.

Accordingly, the sensorless control method according to embodiments ofthe present disclosure compensates the error (α) using the angle errorcompensator 130 before the electrical angle error (Δθ+α) is inputtedinto the PLL controller 150 (S300). When the error (α) is compensated bythe angle error compensator 130, the PLL controller 150 estimates anactual angle of the motor 10 by reducing the electrical angle error(S400), and then controls the motor 10 in an ultra-high speed regionthereof using the estimated actual angle (S500).

FIG. 4 is a table drawing comparing a control model for a permanentmagnet motor based on iron loss with a control model therefor not basedon iron loss. Symbols denoted in FIG. 4 are referred to with definitionas follows.

d, q: accurate d, q-axis

ω_(e): electric angular velocity of motor

i_(d): d-axis current

i_(q): q-axis current

i_(di): d-axis iron loss current

i_(qi): q-axis iron loss current

i_(dm): d-axis magnetizing current

i_(qm): q-axis magnetizing current

v_(d): d-axis voltage

v_(q): q-axis voltage

R_(s): stator phase resistance

R_(i): Iron loss equivalent resistance

L_(d): d-axis inductance

L_(q): q-axis inductance

ψ_(m): permanent magnet flux constant

P_(iron): Iron loss

P_(h): hysteresis loss

P_(ed): eddy-current loss

Influence on iron loss of a conventional permanent magnet motor may beresearched to check influence on iron loss of the motor 10 according toembodiments of the present disclosure.

FIG. 4 is a drawing illustrating d-axis and q-axis models of a motor notbased on iron loss, as well as d-axis and q-axis models based on ironloss.

As shown in FIG. 4, resistance of a resistor R_(i) is equivalent to ironloss, and the resistor R_(i) is connected in parallel to an inductor ofa motor. Therefore, a motor model based on iron loss is different from amotor model not based on iron loss, since the sensorless control methodnot based on iron loss is not able to accurately measure an angle forcontrolling a motor.P _(iron) =P _(h) +P _(ed)

Iron loss (P_(iron)) may respectively be divided into hysteresis loss(P_(h)) and Iron, eddy current loss (P_(ed)). The hysteresis loss isproportional to frequency of the current applied to the motor, and theeddy current loss is proportional to the square thereof. Because afrequency applied to the ultra-high-speed motor is twice or more higherthan a frequency applied to a typical high-speed motor, iron loss of theultra-high-speed motor is four times or more higher than iron loss ofthe typical high-speed motor. Accordingly, to control anultra-high-speed motor, it is necessary to consider iron loss, as isdescribed herein.

FIG. 5 is a graph illustrating a voltage equation of a motor in anordinary axis and an inclined axis.

A conventional voltage equation of a motor with respect to the ordinaryaxis may utilize the following equation (a), and a voltage equation ofthe motor based on iron loss with respect to the ordinary axis accordingto embodiments of the present disclosure may utilize the followingequation (b).

$\begin{matrix}{\mspace{79mu}{\begin{bmatrix}v_{d} \\v_{q}\end{bmatrix} = {{\begin{bmatrix}{R_{s} + {pL}_{d}} & {{- \omega_{e}}L_{q}} \\{\omega_{e}L_{d}} & {R_{s} + {pL}_{q\;}}\end{bmatrix}\begin{bmatrix}i_{d} \\i_{q}\end{bmatrix}} + \begin{bmatrix}0 \\{\omega_{e}\psi_{m}}\end{bmatrix}}}} & {{Equation}\mspace{14mu}(a)} \\{\begin{bmatrix}v_{d} \\v_{q}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{d} \\i_{q}\end{bmatrix} + \begin{bmatrix}\frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \\{\omega_{e}\psi_{m}}\end{bmatrix}}}}} & {{Equation}\mspace{14mu}(b)}\end{matrix}$

e_(γ): estimated d-axis extended EMF

e_(δ): estimated q-axis extended EMF

e′_(γ): estimated d-axis extended EMF considering iron loss

e′_(δ): estimated q-axis extended EMF considering iron loss

According to whether iron loss of the motor 10 is considered, thevoltage equations (a) and (b) are different from each other. Because ofnot being able to actually know a d-axis and a q-axis of the motor, aγ-axis and a δ-axis that respectively estimate the d-axis and the q-axisare substantially used. Voltage equations of the motor with respect tothe inclined axis may respectively utilized the following equations (c)and (d). The following equation (c) corresponds to a conventionalvoltage equation of the motor not based on iron loss, and the followingequation (d) corresponds to a voltage equation of the motor based oniron loss according to embodiments of the present disclosure.

$\begin{matrix}{\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + {pL}_{d}} & {{- \omega_{e}}L_{q}} \\{\omega_{e}L_{q}} & {R_{s} + {pL}_{d}}\end{bmatrix}{\quad{{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \begin{bmatrix}{{E_{ex}\sin\;{\Delta\theta}} - {\left( {{\hat{\omega}}_{e} - \omega_{e}} \right)L_{d}i_{\delta}}} \\{{E_{ex}\cos\;{\Delta\theta}} + {\left( {{\hat{\omega}}_{e} - \omega_{e}} \right)L_{d}i_{\gamma}}}\end{bmatrix}} = e_{\gamma\delta}}}}} & {{Equation}\mspace{14mu}(c)} \\{\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{{\begin{bmatrix}i_{d} \\i_{q}\end{bmatrix} + \begin{bmatrix}{{\frac{w_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} \\{{{- \frac{w_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}}\end{bmatrix}} = {{e_{\gamma\delta}^{\prime}\mspace{85mu} E_{ex}} = {{\omega_{e}\left\{ {{\left( {L_{d} - L_{q}} \right)i_{d}} + \psi_{m}} \right\}} - {\left( {L_{d} - L_{q}} \right)\left( {pi}_{q} \right)}}}}}}} & {{Equation}\mspace{14mu}(d)}\end{matrix}$

FIG. 6 is a schematic drawing comparing an internal logic of the backEMF observer 110 according to embodiments of the present disclosure witha conventional internal logic of the back EMF observer 110A not based oniron loss.

According to whether iron loss of the motor 10 is considered, since theback EMF equations (e) and (f) of the back EMF observer are differentfrom each other, the internal logic of the back EMF observer 110A shouldbe modified to be the internal logic of the back EMF observer 110. Thefollowing equation (e) corresponds to a conventional back EMF equation,and the following equation (f) corresponds to a back EMF equationaccording to embodiments of the present disclosure.

When the conventional back EMF observer 110A is used, since a back EMFdetermination is not appropriately performed, an electrical angle errormay occur.

$\begin{matrix}{\mspace{79mu}{\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {{\begin{bmatrix}{R_{s} + {pL}_{d}} & {{- \omega_{e}}L_{q}} \\{\omega_{e}L_{q}} & {R_{s} + {pL}_{d\;}}\end{bmatrix}\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix}} + \begin{bmatrix}e_{\gamma} \\e_{\delta}\end{bmatrix}}}} & {{Equation}\mspace{14mu}(e)} \\{\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\quad{\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}^{\prime}\end{bmatrix}}}}}} & {{Equation}\mspace{14mu}(f)}\end{matrix}$

Referring to FIG. 2, even though the back EMF observer 110 accuratelyestimates a back EMF of the motor and calculates an electrical angleerror thereof, an additional electrical angle error by α occurs as inthe following equation (h) in case of based on iron loss of the motor.The following equation (g) is a conventional equation not based on ironloss of the motor. Since iron loss of the motor is not included in thefollowing equation (g), an additional electrical angle error (α) doesnot exist therein.

In embodiments of the present disclosure, the additional electricalangle error (α) may be obtained by simulating and/or testing a motor,and the obtained additional electrical angle error (α) may becompensated by the angle error compensator 130.e _(γ) =E _(ex) sin Δθ−({circumflex over (ω)}_(e)−ω_(e))L _(d) i _(δ)e _(δ) =E _(ex) cos Δθ+({circumflex over (ω)}_(e)−ω_(e))L _(d) i_(γ)Δθ=tan⁻¹(e _(γ) /e _(δ))   Equation (g)

$\begin{matrix}{{e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}}{e_{\delta}^{\prime} = {{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}}\mspace{79mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{34mu}\alpha} = {\tan^{- 1}\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}}}} & {{Equation}\mspace{14mu}(h)}\end{matrix}$

As described above, according to embodiments of the present disclosure,it is possible to stably perform sensorless control in anultra-high-speed driving region of a motor by adding a control modelconsidering iron loss of the motor to a back EMF observer and obtainingan accurate electrical angle error based on the iron loss through thecontrol model. Further, according to embodiments of the presentdisclosure, it is possible to improve performance of a motor byconsidering iron loss of the motor through a back EMF observer,compensating for an EMF of the motor based on the considered iron loss,calculating an accurate electrical angle error using the compensatedEMF, and using the accurate electrical angle error in control of themotor.

Embodiments of the present disclosure may have advantages as follows.

Stability: it is possible to stably control a motor in anultra-high-speed driving region of more than about 50,000 rpm throughestimating accurate angle associated with driving of the motor.

Enhanced efficiency: it is possible to reduce an electrical burdenloaded on a motor by efficiently using back EMF of the motor, therebyenhancing efficiency of an ultra-high-speed motor system.

Enlarged drivability: it is possible to drive a motor even in anultra-high-speed driving region of more than about 100,000 rpm byaccurately calculating a driving angle of a motor. (It is difficult todrive a motor in an ultra-high-speed driving region of more than about50,000 rpm in the related art.)

Improved performance: it is possible to improve efficiency of d-axis andq-axis current and voltage control based on accurate angle informationwith respect to a motor, thereby improving torque and power performanceof the motor.

While the embodiments have been described in connection with a permanentmagnet motor for a turbocharger, the embodiments may be applied to anultra-high-speed motor for a micro-turbine generator, anultra-high-speed motor for a circular compressor, an ultra-high-speedmotor for a pump, and so on. Therefore, the description of the permanentmagnet motor herein should not be treated as limited the applicabilityof the present disclosure.

While this disclosure has been described in connection with what ispresently considered to be practical embodiments, it is to be understoodthat the disclosure is not limited to the disclosed embodiments, but, onthe contrary, is intended to cover various modifications and equivalentarrangements included within the spirit and scope of the appendedclaims.

DESCRIPTION OF REFERENCE NUMERALS

-   -   10: motor    -   110: back electromotive force (EMF) observer    -   120: angle error calculator    -   130: angle error compensator    -   150: phase locked loop (PLL) controller

What is claimed is:
 1. A sensorless control method for a motor performedby a sensorless controller including a back electromotive force (EMF)observer and a phase locked loop (PLL) controller, comprising:estimating a back EMF of the motor using the back EMF observer;calculating an electrical angle error in accordance with iron loss ofthe motor based on the estimated back EMF; compensating for thecalculated electrical angle error; inputting the compensated electricalangle error into the PLL controller to estimate an actual angle; andcontrolling the motor based on the estimated actual angle.
 2. Thesensorless control method of claim 1, wherein voltages (v_(γ), v_(δ)) ofthe motor based on the iron loss are calculated using the followingequation: $\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \begin{bmatrix}{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} \\{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}}\end{bmatrix}} = {{e_{\gamma\delta}^{\prime}\mspace{79mu} E_{ex}} = {{\omega_{e}\left\{ {{\left( {L_{d} - L_{q}} \right)i_{d}} + \psi_{m}} \right\}} - {\left( {L_{d} - L_{q}} \right)\left( {pi}_{q} \right)}}}}}}$d, q: accurate d, q-axis ω_(e): electric angular velocity of motori_(d): d-axis current i_(q): q-axis current i_(di): d-axis iron losscurrent i_(qi): q-axis iron loss current i_(dm): d-axis magnetizingcurrent i_(qm): q-axis magnetizing current v_(d): d-axis voltage v_(q):q-axis voltage R_(s): stator phase resistance R_(i): Iron lossequivalent resistance L_(d): d-axis inductance L_(q): q-axis inductanceψ_(m): permanent magnet flux constant P_(iron): Iron loss P_(h):hysteresis loss P_(ed): eddy-current loss e_(γ): estimated d-axisextended EMF e_(δ): estimated q-axis extended EMF e′_(γ): estimatedd-axis extended EMF considering iron loss e′_(δ): estimated q-axisextended EMF considering iron loss.
 3. The sensorless control method ofclaim 1, wherein the back EMF observer estimates voltages (v_(γ), v_(δ))of the motor using the following equation: $\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + {\begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}^{\prime}\end{bmatrix}.}}}}$
 4. The sensorless control method of claim 1, whereinthe electrical angle error (Δθ+α) is calculated using the followingequation:$e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}$$e_{\delta}^{\prime} = {{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}$$\mspace{20mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{34mu}\alpha} = {{\tan^{- 1}\left( \frac{w_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}.}}}$5. The sensorless control method of claim 1, wherein the inputting ofthe compensated electrical angle error into the PLL controller toestimate the actual angle comprises reducing the electrical angle errorbased on the iron loss.
 6. A sensorless control system controlling amotor including a permanent magnet motor, comprising: a back EMFobserver configured to estimate a back EMF of the motor; an angle errorcalculator configured to calculate an electrical angle error inaccordance with iron loss of the motor based on the estimated back EMF;an angle error compensator configured to compensate for the calculatedelectrical angle error; and a PLL controller configured to: i) receivethe compensated electrical angle error, ii) estimate an actual angle,and iii) control the motor based on the estimated actual angle.
 7. Thesensorless control system of claim 6, wherein voltages (v_(γ), v_(δ)) ofthe motor based on the iron loss are calculated by the followingequation: $\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + \mspace{371mu}\begin{bmatrix}{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} \\{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}}\end{bmatrix}} = {{e_{\gamma\delta}^{\prime}\mspace{79mu} E_{ex}} = {{\omega_{e}\left\{ {{\left( {L_{d} - L_{q}} \right)i_{d}} + \psi_{m}} \right\}} - {\left( {L_{d} - L_{q}} \right)\left( {pi}_{q} \right)}}}}}}$d, q: accurate d, q-axis ω_(e): electric angular velocity of motori_(d): d-axis current i_(q): q-axis current i_(di): d-axis iron losscurrent i_(qi): q-axis iron loss current i_(dm): d-axis magnetizingcurrent i_(qm): q-axis magnetizing current v_(d): d-axis voltage v_(q):q-axis voltage R_(s): stator phase resistance R_(i): Iron lossequivalent resistance L_(d): d-axis inductance L_(q): q-axis inductanceψ_(m): permanent magnet flux constant P_(iron): Iron loss P_(h):hysteresis loss P_(ed): eddy-current loss e_(γ): estimated d-axisextended EMF e_(δ): estimated q-axis extended EMF e′_(γ): estimatedd-axis extended EMF considering iron loss e′_(δ): estimated q-axisextended EMF considering iron loss.
 8. The sensorless control system ofclaim 6, wherein the back EMF observer is further configured to estimatevoltages (v_(γ), v_(δ)) using the following equation: $\begin{bmatrix}v_{\gamma} \\v_{\delta}\end{bmatrix} = {\begin{bmatrix}{R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}} & {{{- \omega_{e}}L_{q}} + {p\;\frac{\omega_{e}L_{d}L_{q}}{R_{i}}}} \\{{\omega_{e}L_{q}} - {p\;\frac{\omega_{c}L_{d}L_{q}}{R_{i}}}} & {R_{s} + \frac{\omega_{e}^{2}L_{d}L_{q}}{R_{i}} + {pL}_{d}}\end{bmatrix}{\quad{\begin{bmatrix}i_{\gamma} \\i_{\delta}\end{bmatrix} + {\begin{bmatrix}e_{\gamma}^{\prime} \\e_{\delta}^{\prime}\end{bmatrix}.}}}}$
 9. The sensorless control system of claim 6, whereinthe angle error calculator is further configured to calculate theelectrical angle error (Δθ+α) using the following equation:$e_{\gamma}^{\prime} = {{{\frac{\omega_{e}^{2}L_{d}{\psi\;}_{m}}{R_{i}}\cos\;{\Delta\theta}} + {E_{ex}\sin\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\sin\left( {{\Delta\theta} + \alpha} \right)}}}$$e_{\delta}^{\prime} = {{{{- \frac{\omega_{e}^{2}L_{q}{\psi\;}_{m}}{R_{i}}}\sin\;{\Delta\theta}} + {E_{ex}\cos\;{\Delta\theta}}} = {\sqrt{\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}} \right)^{2} + E_{ex}^{2}}{\cos\left( {{\Delta\theta} + \alpha} \right)}}}$$\mspace{20mu}{{{\Delta\theta} + \alpha} = {{{\tan^{- 1}\left( \frac{e_{\gamma}^{\prime}}{e_{\delta}^{\prime}} \right)}\mspace{34mu}\alpha} = {{\tan^{- 1}\left( \frac{\omega_{e}^{2}L_{q}\psi_{m}}{R_{i}E_{ex}} \right)}.}}}$10. The sensorless control system of claim 6, wherein the PLL controlleris further configured to estimate the actual angle by reducing theelectrical angle error based on the iron loss.